Material Derivative - Orthogonal Coordinates

Orthogonal Coordinates

It may be shown that, in orthogonal coordinates, the component of convection is given by:

$_j = \sum_i \frac{v_i}{h_i} \frac{\partial u_j}{\partial q^i} + \frac{u_i}{h_i h_j}\left(v_j \frac{\partial h_j}{\partial q^i} - v_i \frac{\partial h_i}{\partial q^j}\right),$